Rupture directivity of micro-earthquakes along the San Andreas fault

Theoretically, it is expected that earthquakes occurring on an interface separating materials with different elastic properties might have a preferential rupture propagation direction. To test for this, we searched for indications of directivity by examining spectral ratios of multiple pairs of nearby earthquakes at azimuthally distributed seismic stations. By taking the spectral ratios, this technique is capable of canceling path and station terms in seismic spectra. It differs from a typical empirical Green's Function approach in that it compares events with similar sizes as well as events with significant size differences. The spectral ratios are fitted with a simple forward model, in which a bidirectional earthquake source is composed of two point sources moving at constant velocities in opposite directions (assumed to be horizontal). Each bidirectional earthquake has four model parameters: the lengths of the two rupture halves running in opposite directions, and their propagation velocities. A priori information concerning the total rupture length of bidirectional events are computed from catalog magnitude using a moment-magnitude relation and a 3MPa stress drop on an equidimensional rupture. The a priori rupture velocity is peaked at 0.8Vs and constrained to be smaller than Vs. Since identical earthquakes would produce frequency-independent spectral ratios at all azimuths, determining the initiation points of earthquakes requires variability in event size and/or relative directivity. The relocated catalog of Rubin [2002] was used to define 78 clusters of repeating earthquakes along the central San Andreas fault. The spectral ratios of all combinations of earthquake pairs in each cluster were fitted with synthetic spectral ratios at stations with sufficient signal-to-noise ratio and coherence. The inversion results show that, as might have been expected, differences in rupture processes (duration and relative directivity) of the earthquakes within most repeating clusters cannot be resolved. Different rupture durations can be found for some repeating events. Beyond those caused by differences in duration, spectra of 89 events in 15 repeating clusters show clear signals of directivity (consistent azimuthal dependence of spectral ratios). Preliminary results suggest that 33 of the 89 events run unilaterally to the NW, 29 run unilaterally to the SE (theoretically the preferential direction) and the other 27 are bilateral. Thus to date we have found no preferred tendency for rupture propagation to the SE. We will next expand our search to include nearby earthquakes not necessarily belonging to repeating clusters. This will increase to thousands the number of earthquakes we can examine, and will include a larger range of earthquake sizes (and perhaps relative directivity) in the inversion.